A pilot can travel 396 miles with the wind in the same amoun

A pilot can travel 396 miles with the wind in the same amount of time as 324 miles against the wind. Find the speed of the wind if the pilot\'s speed in still air is 220 miles per hour. Be sure to include proper units.

Solution

Let the wind\'s speed be x mph . Then the pilot\'s speed with the wind is 220 + x. The time taken by the pilot to travel 396 miles at the speed of 220 + x mph is 396/ (220 + x)...(1) ( time = distance/speed)

Also, the pilot\'s speed against the wind is 220 - x. The time taken by the pilot to travel 324 miles at the speed of 220 - x mph is 324/ (220 - x)...(2) . Therefore, we have 396/ (220 + x) = 324/ (220 - x) or, (220 + x) / ( 220 - x) = 396/324 = 11/9 or, 9(220 + x ) = 11( 220 - x) or, 1980 + 9x = 2420 - 11x or, 9x + 11x = 2420 - 1980 or, 20x = 440. Therefore, x = 440/20 = 22.